In Olympic running events, preliminary heats are determined by random draw, so we should expect the ability level of runners in the various heats to be about the same, on average. The table gives the times (in seconds) for the 800-m men€™s run in the 2012 Olympics in London for preliminary heats 1 and 3. Is there any evidence that the mean time to finish is different for randomized heats? Explain. Be sure to include a discussion of assumptions and conditions for your analysis.

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Name Nigel Amos Fabiano Pecanha Luis Alberto Marco 106.9 Khadevis Robinson 07.2 Marcin Lewandowski 107.61 Ivan Tukhtachev Derek Mandell Abubaker Kaki Timothy Kitum Abdulaziz Ladan Mohammed Andy González Gareth Warburton Tamás Kazi Sören Ludolph Arnold Sorina Time Heat 105.9 1063 1 Country BOT BRA ESP USA POL RUS GUM SUD KEN KSA 1 109.8 118.91 105.53 105.7 3 106.1 3 CUB GBR HUN GER VAN 106.2 3 107.0 3 107.1 108.63 1143 3